Since 1937, Stan Musial has the best batting average by a Hall of Famer with 20+ home runs with 500+ at-bats in a season, with an average of .376 in 1948.

highest ba in a season by a hall of famer with 20 hr and 500 ab since 1937
Interpreted as:
highest ba in a season by a hall of famer by a player with 20 or more hr and 500 or more ab since 1937

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